Assignment If you drop an anvil from a great height, it accelerates downward...

Question

Assignment

If you drop an anvil from a great height, it accelerates downward... Write a program containing two functions: one that returns v(t) and another that returns y(t) for the anvil. Your program should plot both these functions on one graph, for time ranging from 0 to 5 seconds. Have the program label the axes appropriately and put ANVIL in the title.

Hint

Actually, everything you need code-wise is on this page, except the physics. Don't forget to import matplotlib.pyplot and numpy! Here's a sample program that puts together much of this example code.

Explanation / Answer

import numpy as np

import matplotlib.pyplot as plt

def time_to_hit_ground(y0, v0, a):

discriminant = np.sqrt(v0**2 - 2*a*y0)

t1 = (-v0 - discriminant) / a

t2 = (-v0 + discriminant) / a

if t1 >=0:

return t1

return t2

def drop(y0, v0=0.0, dt=0.1, g=-9.8):

if y0 < 0:

print('Object is underground.')

return

# if you also allow the user to change `dt` and `g` from the arguments,

t_ground = time_to_hit_ground(y0, v0, g)

t = np.arange(0, t_ground+dt, dt)

v = v0 + g * t

y = y0 + v0 * t + g * t**2 / 2.

plt.plot(t, y, '.')

plt.axvline(t_ground, color='g')

plt.axhline(0, color='g')

plt.xlabel('Time (s)')

plt.ylabel('Height (m)')

plt.show()

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